OPT Offer letter and No paystubs

I have undergone training from a consultancy in US and they are currently working on marketing my resume.

I have already accumulated 55 days of unemployment on my OPT. My consultancy told me that they will give me a offer letter that I can submit at ISS office in my school which will help me maintain my Status.

When I asked my consultancy if they will run my payroll since the offer letter start date, they were hesitant and said I-9 form will be completed and payroll will be run only after I get a project.

How does this affect my immigration status? What if USCIS requests for paystubs when I apply for H1 in April 2015?

I tried applying in lot of US companies directly but they all require only US citizens or GC holders, they were not willing to sponsor fresh H1. So it seems like desi consultancy is the route to take.

Any comments will be helpful in making a decision.

F1 student